LSODA.jl is a Julia package that interfaces to the liblsoda library, developed by Simon Frost (@sdwfrost), thereby providing a way to use the LSODA algorithm from Linda Petzold and Alan Hindmarsh from Julia. Clang.jl has been used to write the library and Sundials.jl was a inspiring source.
To install this package, run the command
To solve an ODE, one can call the simplified solver:
function rhs!(t, x, ydot, data) ydot=1.0E4 * x * x - .04E0 * x ydot=3.0E7 * x * x ydot=-ydot - ydot nothing end y0 = [1.,0.,0.] tspan = [0., 0.4] res = lsoda(rhs!, y0, tspan, reltol= 1e-4, abstol = Vector([1.e-6,1.e-10,1.e-6]))
To reproduce the test example from liblsoda, on can use:
lsoda_0(rhs!, y0, tspan, reltol= 1e-4, abstol = Vector([1.e-6,1.e-10,1.e-6]))
This should give the following.
at t = 4.0000e-01 y= 9.851712e-01 3.386380e-05 1.479493e-02 at t = 4.0000e+00 y= 9.055333e-01 2.240655e-05 9.444430e-02 at t = 4.0000e+01 y= 7.158403e-01 9.186334e-06 2.841505e-01 at t = 4.0000e+02 y= 4.505250e-01 3.222964e-06 5.494717e-01 at t = 4.0000e+03 y= 1.831976e-01 8.941774e-07 8.168016e-01 at t = 4.0000e+04 y= 3.898729e-02 1.621940e-07 9.610125e-01 at t = 4.0000e+05 y= 4.936362e-03 1.984221e-08 9.950636e-01 at t = 4.0000e+06 y= 5.161832e-04 2.065786e-09 9.994838e-01 at t = 4.0000e+07 y= 5.179811e-05 2.072030e-10 9.999482e-01 at t = 4.0000e+08 y= 5.283524e-06 2.113420e-11 9.999947e-01 at t = 4.0000e+09 y= 4.658945e-07 1.863579e-12 9.999995e-01 at t = 4.0000e+10 y= 1.423392e-08 5.693574e-14 1.000000e+00
JuliaDiffEq Common Interface
The functionality of LSODA.jl can be accessed through the JuliaDiffEq common interface. To do this, you build a problem object for like:
using DiffEqBase function rhs!(t, x, ydot, data) ydot=1.0E4 * x * x - .04E0 * x ydot=3.0E7 * x * x ydot=-ydot - ydot nothing end y0 = [1.,0.,0.] tspan = (0., 0.4) prob = ODEProblem(rhs!,y0,tspan)
This problem is solved by LSODA by using the lsoda() algorithm in the common
solve command as follows:
sol = solve(prob,lsoda())
Many keyword arguments can be used to control the solver, its tolerances, and its output formats. For more information, please see the DifferentialEquations.jl documentation.